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3 years ago

Estimate the decimal expression -0.54+(-0.8720

Mathematics

1 answer:

yan [13]3 years ago

7 0

Answer:

-1.412

Step-by-step explanation:

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(1) Find the torsion of the helix a(t) = (cos(t), sin(t), t)

Kitty [74]

Answer:

The torsion of the helix is $\tau=\frac{1}{2}$ .

Step-by-step explanation:

To complete this exercise we need to recall the formula for the torsion of a curve. Given a parametrization $r(t) = (x(t), y(t), z(t))$ the torsion of the curve is given by

$\tau = \frac{(r'\times r'')\cdot r'''}{\|r'\times r''\|^2}$ .

So, the first step is to find the derivatives of the vector function $r$ .

Thus,

$r(t)=(\cos t,\sin t, t)$ ,

$r'(t) = (-\sin t, \cos t, 1)$ ,

$r''(t) = (-\cos t, -\sin t, 0)$ ,

$r'''(t)=(\sin t, -\cos t,0)$ .

Now, we must calculate the cross product of the vector functions $r'$ and $r''$ .

$r'(t)\times r''(t)=\begin{vmatrix}i& j & k\\ -\sin t & \cos t & 1\\ -\cos t & -\sin t & 0\end{vmatrix} = i\begin{vmatrix} \cos t & 1\\ -\sin t & 0\end{vmatrix} -j\begin{vmatrix} -\sin t & 1\\ -\cos t & 0\end{vmatrix}+k\begin{vmatrix} -\sin t & \sin t\\ -\cos t & -\sin t\end{vmatrix}$

$r'(t)\times r''(t) = i\sin t -j\cos t +k(\sin^2t+\cos^2t) = i\sin t -j\cos t +k$ .

Now we calculate $\|r'\times r''\|^2$ :

$\|r'\times r''\|^2 = \sin^2t+\cos^2t+1=2$

Recall that the norm of a vector in the space $\mathbb{R}^3$ is

$\|(x,y,z)\|^2 = x^2+y^2+z^2$ .

At this point we have

$\tau = \frac{1}{2}\left((i\sin t -j\cos t +k)\cdot (i\sin t -j\cos t+0k)\right) = \frac{1}{2}\left(\sin^2t+\cos^2t\right) =\frac{1}{2}$ .

6 0

3 years ago

Elena has $5 and sells pens for $1.50 each. She wants to

Alexxandr [17]

Answer:

10 pens

Step-by-step explanation:

Find out how much pens she needs to sell to get $15, to get $15, exclude out how much Elena has.

$20 - $5 = $15

Now divide.

$15.00 ÷ $1.50 = 10 pens

4 0

3 years ago

Read 2 more answers

A local fast-food restaurant can serve

Marizza181 [45]

Answer:

4 hours, 150 x 4 = 600 pls give brainliest

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3 years ago

In a set of 10 observations the mean is 20 and the median is 15. There are 2 values that are 6, and all other values are differe

Kitty [74]

The mode of the set of 10 observations is 2.

What is the mode?

Mode refers to a value that appears most frequently in a data set. Mode is a measure of central tendency of a data set. Other measures of central tendency are mean and median.

According to the information in the question, 6 appears twice in the data set and all other values are different. Thus, 6 has the frequency of 2 which is the highest. 6 is the mode.

To learn more about mode, please check: brainly.com/question/16505756

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7 0

2 years ago

When n=8, what is the value of 3 x n-8? A. 0 B. 3 C. 16 D. 19

tamaranim1 [39]

Answer:

there is no correct answer

Step-by-step explanation:

PEMDAS- fisrt parenthesis, then exponents, then multiplication or division, then lastly addition or subtraction

3×8-8

24-8

the answers given are subtracting the eights first, in which case the answe would be A. 0

3×8-8

3×0

5 0

3 years ago